WATER RESOURCES RESEARCH, VOL. 37, NO. 12, PAGES 3349 –3358, DECEMBER 2001
Experimental study of the transport of mixed sand and gravel
Peter R. Wilcock, Stephen T. Kenworthy, and Joanna C. Crowe
Department of Geography and Environmental Engineering, Johns Hopkins University
Baltimore, Maryland, USA
Abstract. We measured a wide range of transport rates for five different sand/gravel
mixtures in a laboratory flume. Each mixture used the same gravel, and sand was added to
produce mixtures containing 6, 15, 21, 27, and 34% sand. Control of other variables allows
us to isolate the effect of bed sand content on transport. As sand content increases, gravel
transport rates increase by orders of magnitude, even though the proportion of gravel in
the bed decreases. The increase in gravel transport rate is most rapid over the range of
bed sand content between 15 and 27%. The increase in transport rate is larger than
predicted using standard scaling relations between transport rate and grain size, indicating
that models of transport and sorting and predictions of stream channel response to sand
inputs need to be revised to account for the influence of sand content. Bed surface grain
size was measured at the end of each run. Surface grain size varied with sand content but
showed little or no coarsening with flow strength and transport rate. This casts doubt on
the idea that armor layers form at small flows and weaken or vanish with increasing flow
and transport rate.
1.
Introduction
A variety of natural or human actions, such as fire, logging,
flow diversion, road construction, and urban or agricultural
development can increase the supply of sand to a gravel bed
river. An understanding of the river channel’s response to sand
inputs, as well as the fate of the sand, requires an understanding of the effect of sand content on transport rate. Previous
work [Jackson and Beschta, 1984; Ikeda and Iseya, 1988; Wilcock, 1998] provides some indication that increased sand content can augment gravel transport rates beyond that which can
be adequately accounted for in standard transport models. The
purpose of the experiments described in this paper is to document the effect of river bed sand content on the transport
rates of sand and gravel.
We measured flow and transport in four series of flume runs
using a gravel sediment to which sand was added to produce
mixtures containing 6, 15, 21, and 27% sand. The gravel and
sand component of each mixture was identical: The gravel
ranged in size from 2 to 64 mm with median 13 mm, and the
sand size range was 0.5 to 2.0 mm with median 1 mm. For each
of the four sediments, 9 or 10 flume runs were conducted over
a range of water discharge. Each run was continued until the
flow and transport reached a steady state, at which point flow
rate, depth, and slope were measured along with transport
rates of different size fractions. Combined with the results of
earlier experiments conducted with the same gravel mixed with
34% sand in the 0.21–2.0 mm range [Wilcock and McArdell,
1993], the experimental results discussed here provide a direct
evaluation of the effect of sand content on transport over a
range of transport rates and for a range of sand content that
encompasses much of the variation observed in natural
streams.
In addition to measuring transport rate, we also measured
the size distribution of the bed surface at the end of each run,
Copyright 2001 by the American Geophysical Union.
Paper number 2001WR000683.
0043-1397/01/2001WR000683$09.00
giving coupled observations of transport rate, bed surface composition, and flow. This is the information needed to develop
an empirical model of transport rate referenced to the grains
immediately available for transport on the bed surface. As
discussed in detail elsewhere [e.g., Parker, 1990; Wilcock and
McArdell, 1993; Wilcock, 2001], a general model for mixed-size
sediment transport must be referenced to the bed surface composition in order to predict size sorting and transient adjustments of the flow/bed/transport system. The data presented
here are the first comprehensive collection of coupled observations of transport rate, surface composition, and flow for a
range of sediments. Previous field investigations have generally
been limited to a single observation of bed surface composition
at low flow; the bed composition associated with active transport is generally unknown. Some previous laboratory transport
studies have included measurements of the bed surface composition, although the samples were collected using adhesives,
which introduces uncertainty about the inclusion of subsurface
sediment in the sample and which requires a conversion to
allow comparison with transport and subsurface samples. We
measure the surface with a simple point count method that
permits direct comparison with volume-by-weight samples of
the transport [Church et al., 1987]. That the surface-based
transport observations are made for a series of sediments defined by a controlled variation in sand content is an added
benefit. Because surface-based transport observations require
special effort and are relatively rare, the data discussed here
are available as an AGU electronic supplement.1
2.
Previous Experiments
Previous experiments shed light on how gravel transport
rates respond to a change in sand supply. Jackson and Beschta
[1984] deposited a sandy gravel bed in a flume and, in a series
1
Supporting tables are available via Web browser or via Anonymous
FTP from ftp://agu.org, directory “apend” (Username ⫽ “anonymous”, Password ⫽ “guest”); subdirectories in the ftp site are arranged
by paper number. Information on searching and submitting electronic
supplements is found at http://www.agu.org/pubs/esupp_about.html.
3349
3350
WILCOCK ET AL.: STUDY OF TRANSPORT OF MIXED SAND AND GRAVEL
in the field typically contain intermodal sediment. The Froude
numbers in the experiments were much larger than typically
found under conditions of alluvial transport, and the very shallow (⬇1 cm) flow depth limited the accuracy of depth measurements. Despite these problems the experiments of Ikeda
and Iseya show unequivocally that gravel transport rates can be
maintained or even augmented in the presence of additional
sand.
The experiments presented here build on this previous work
in several ways. First, the size range of the experimental sediment (0.5– 64 mm) is unusually large for a flume study and is
directly representative of many gravel bed rivers. Second, a
wide range of transport rates was measured for each sediment,
allowing us to examine the influence of sand content on not
just a single transport rate but on the trend between transport
rate and flow strength. Third, the bed surface grain-size distribution was measured at the end of each run, providing a
measure of the bed response to varying flow and sand content.
Finally, sediment was recirculated in the present experiments,
providing a direct comparison between the composition of the
bed and the resulting transport.
Figure 1. Results of experiments by Ikeda and Iseya [1988].
As sand is added to gravel feed, the stress needed to transport
the sediment decreases even though the rate of transport is
larger.
of eight runs, allowed the deposit to armor by running clear
water over the bed until no further sediment emerged from the
flume. Sand was then added to the clear water inflow, and
additional gravel was transported out of the channel, demonstrating that additional sand was able to induce entrainment
and transport from an armored gravel bed.
The clearest demonstration of the effect of sand on gravel
transport has been achieved with eight runs in a small flume
(10 cm wide) by Ikeda and Iseya [1988]. In the first five runs
they fed fine gravel (2.7 mm) at a rate that increased from run
to run. The discharge was held constant, and the depth varied
little, so as the feed rate increased, the bed slope increased to
produce a larger bed shear stress to carry the larger transport
rate (Figure 1). For the last three runs the rate of gravel input
was held constant, and well-sorted medium sand (0.35 mm)
was also fed into the flume, thereby increasing the total feed
rate. The bed slope decreased, indicating that a smaller shear
stress was needed to transport the sand-gravel mixture, even
though the transport rate of the gravel remained unchanged
and the total transport rate increased. This demonstrates that
the same amount of gravel could be transported at the same
flow, even though additional sand is added to the system. In
fact, the decrease in shear stress indicates that more gravel
could be carried with the same shear stress if sand is added to
the system.
Although indicative, there are several aspects of the Ikeda
and Iseya experiments that limit direct extrapolation to the
field case. The sediment used (0.37 and 2.6 mm) was much
smaller than typical sediment in a gravel bed river, particularly
in the gravel fraction, and the difference in size between the
sand and gravel fractions was also very small. The sediment
size distribution was also strongly bimodal with no overlap
between the modes, whereas even strongly bimodal sediments
3.
Methods
3.1.
Sediment
The experimental sediments were prepared by adding different amounts of sand to a gravel mixture (Table 1 and Figure
2). The gravel ranged in size from 2.0 to 64 mm and is identical
to the gravel portion of the bed of many colors (BOMC)
sediment previously reported on by Wilcock and McArdell
[1993, 1997]. In four of the sediments the sand varied in size
between 0.5 and 2.0 mm. Approximately one half of the sand in
the fifth sediment (BOMC) was in the range of 0.21– 0.5 mm,
making the sand size approximately half that of the other four
(Table 1). The proportion of sand in the mixtures varied from
6.2 to 34.3%; the four new sediments were named according to
the target sand content such that the sediment name and actual
sand content were J06 (6.2%), J14 (14.9%), J21 (20.6%), and J27
(27%). Standard 1/2␾ size fractions were used to define all fractions coarser than 1.0 mm; grains in the 0.5–1.0 mm range were
combined into one fraction.
The mean specific gravity of all size fractions was 2.61; the
maximum deviation from this mean was 5%. The 4.0 – 8.0 mm
size fractions contain some chalky limestone clasts, which lowers the mean density for these fractions to 2.49. The clasts
between 8.0 and 32 mm contain a larger proportion of magic
Table 1. Grain-Size Statistics
Mean,
mm
Standard
Deviation
␾
Median
D 50 ,
mm
D 90 ,
mm
Gravel
Sand
Sand (BOMC)a
12.2
1.0
0.5
1.28
0.53
0.82
13.4
1.0
0.5
39
1.7
1.35
J06
J14
J21
J27
BOMC
10.5
8.4
7.3
6.1
4.1
1.54
1.77
1.88
1.96
2.41
12.2
9.8
8.4
6.7
5.3
38
37
36
33
31
a
BOMC, bed of many colors.
WILCOCK ET AL.: STUDY OF TRANSPORT OF MIXED SAND AND GRAVEL
Figure 2. Grain-size distribution of the experimental sediments.
minerals and have a mean specific gravity in the range 2.69 –
2.73.
3.2.
Transport and Hydraulic Measurements
We conducted 38 experimental runs with the four new mixtures. Combined with 10 BOMC runs, the 48 experimental
runs reported here span a threefold range in water discharge
and a 7 order-of-magnitude range in transport rate. The mean
hydraulic and transport observations for each run are given in
Table 2. The complete size distributions of the bed surface and
transport are available in the AGU electronic supplement.
The experiments were conducted in a tilting laboratory
flume with clear sidewalls. The channel is 60 cm wide with a
working length of 790 cm. A 120 cm artificially roughened bed
was placed at the upstream of the working section to develop
the boundary layer before the flow encounters the loose sediment bed. Downstream of the working section is a 120 cm long,
full-width sediment trap. Water and sediment were recirculated separately. Water temperature was typically between
19⬚C and 23⬚C. Most of the water passed with no overfall over
the sediment trap and into a tailbox and then through two or
three centrifugal pumps and a 20 cm pipe to the upstream end
of the flume. A small portion of the water discharge and the
sediment finer than 16 mm passed through the sediment trap
and was recirculated with an air-driven diaphragm pump
through a 5 cm plastic hose to the flume head box. Coarser
grains were caught on a 16 mm screen inside the sediment trap
and manually returned to the flume head box at periods ranging from 1 to 5 min, depending on transport rate.
Sediment transport was sampled with three different meth-
3351
ods, a result of the separate recirculation paths of the fine and
coarse grains and the competing requirements that we minimize disturbance of the transport during a run while also collecting enough samples to adequately measure the transport
rates. Grains finer than 16 mm were sampled by diverting the
sediment recirculation line to an open hose and directing the
discharge onto a 0.21 mm sieve placed inside a 100 L funnel.
All of the sediment was retained on the sieve, while the water
was immediately returned to the sediment recirculation system
through a hose at the base of the funnel. This system allowed
the transport to be sampled over a wide range of periods,
depending on the transport rate.
Because total transport rate varies over a much wider range
than the transport size distribution, the sampling period necessary to obtain a reliable estimate of the total transport rate is
much longer than that needed to determine the transport size
distribution. During most of a transport sample period, only
the total volume of transported sediment was measured, and
the sample was then returned to the recirculation line through
the sampling funnel within a period of 30 – 60 s. This procedure
permits measurement of the total transport rate with negligible
disruption of the recirculating transport system. Samples for
size analysis were collected at the end of a run to determine the
grain size of the transport and the conversion from volumetric
to mass transport rate. These samples were returned to the
flume prior to the next run. Fractional transport rates are
calculated as q bi ⫽ ( p i )q b , where p i is the proportion of each
fraction in transport and q b is the total transport rate.
The coarser sediment caught on the screen in the sediment
trap was recirculated by hand and was sampled nearly continuously. The gravel fractions were separated by size, and the
mass of each coarse fraction was typically determined with a
hanging balance. On some occasions the number of grains of
each size were counted, and a calibrated number-to-mass conversion was used to determine transport rate. An advantage of
manual recirculation is that we could monitor the rare motion
of the coarsest grains throughout the run, providing a long time
series and a more reliable estimate of their transport rate.
The elevation of the water and bed surfaces during a run
were measured with point gages and referenced to the horizontal plane of a still water surface. Discharge was measured
with a Venturi meter in the water return pipe. Water discharge
in the sediment recirculation line took one of two nearly constant values, depending on whether the sediment pump was
driven by compressed air from the building supply or from a
portable air compressor used to increase sediment recirculation capacity at high transport rates. In both cases the sediment
recirculation discharge was a small fraction of the main water
discharge. Mean flow velocity was determined from the discharge, the mean flow depth, and flume width. Surface velocity
was measured by timing the travel of surface tracers over a 5 m
distance. Plastic bottle caps each with a thickness of 1.5 cm and
a diameter of 3 cm were used as tracers because they were
found to float fully submerged with the upper side just at the
water surface. The mean of the five fastest times out of 10
observations was used to determine the surface velocity. Tracer
tracks within 10 cm of the wall were discarded. Following the
first seven runs of the J06 series, it was found that the manometer used to determine the pressure drop on the Venturi meter
was not properly bled and that the calculated discharge was
apparently too small. For these runs we estimate the mean flow
velocity based on a regression between mean velocity and surface velocity, which showed a tight correlation for all subse-
3352
WILCOCK ET AL.: STUDY OF TRANSPORT OF MIXED SAND AND GRAVEL
Table 2. Mean Flow and Transport Observations
Unit
Discharge,
m2 s⫺1
Flow
Depth,
m
Water
Slope
Bed Shear
Stress, Pa
Gravel
Transport,
g m⫺1 s⫺1
Sand
Transport,
g m⫺1 s⫺1
J06-1
J06-2
J06-3
J06-4
J06-5
J06-6
J06-7
J06-8
J06-9
J06-10
0.0781
0.0862
0.0959
0.1032
0.0906
0.1048
0.1212
0.0778
0.1282
0.1334
0.104
0.108
0.104
0.102
0.103
0.103
0.106
0.105
0.109
0.108
0.0044
0.0049
0.0094
0.0133
0.0067
0.0092
0.0158
0.0056
0.0176
0.0204
4.10
4.90
8.70
11.3
6.18
8.29
16.0
5.42
17.5
23.6
2.09E ⫺ 04a
2.52E ⫺ 03
9.23E ⫺ 02
1.40E ⫹ 00
2.01E ⫺ 02
4.29E ⫺ 01
1.45E ⫹ 01
3.29E ⫺ 03
2.95E ⫹ 01
2.04E ⫹ 02
1.33E ⫺ 05
6.17E ⫺ 06
2.36E ⫺ 04
2.90E ⫺ 03
4.44E ⫺ 05
7.98E ⫺ 04
3.17E ⫺ 02
3.26E ⫺ 05
6.21E ⫺ 02
1.57E ⫺ 01
J14-1
J14-2
J14-3
J14-4
J14-5
J14-6
J14-7
J14-8
J14-9
0.1259
0.1243
0.0838
0.1013
0.1103
0.0788
0.0957
0.0909
0.1334
0.117
0.109
0.107
0.104
0.106
0.102
0.106
0.106
0.117
0.0165
0.0173
0.0061
0.0106
0.0144
0.0044
0.0083
0.0076
0.0157
16.5
19.1
6.43
9.74
16.1
4.38
8.63
7.27
20.1
5.08E ⫹ 01
7.29E ⫹ 01
2.91E ⫺ 02
1.70E ⫹ 00
1.19E ⫹ 01
1.81E ⫺ 02
1.48E ⫹ 00
5.08E ⫺ 01
1.14E ⫹ 02
5.51E ⫺ 01
1.56E ⫹ 00
7.32E ⫺ 04
8.13E ⫺ 02
5.96E ⫺ 01
1.03E ⫺ 03
6.31E ⫺ 02
3.84E ⫺ 02
1.90E ⫹ 00
J21-1
J21-2
J21-3
J21-4
J21-5
J21-6
J21-7
J21-8
J21-9
0.1259
0.0785
0.0888
0.0992
0.0734
0.0903
0.0654
0.1119
0.1203
0.118
0.108
0.102
0.105
0.109
0.104
0.099
0.102
0.107
0.0155
0.0043
0.0071
0.0114
0.0034
0.0078
0.0032
0.0171
0.0175
15.9
4.07
6.64
10.8
3.35
7.21
2.82
16.1
18.6
1.25E ⫹ 02
4.21E ⫺ 01
5.32E ⫹ 00
9.92E ⫹ 00
9.81E ⫺ 02
1.04E ⫹ 01
1.30E ⫺ 02
1.36E ⫹ 02
NAb
9.41E ⫹ 00
6.53E ⫺ 02
8.04E ⫺ 01
2.01E ⫹ 00
3.50E ⫺ 02
2.43E ⫹ 00
3.67E ⫺ 03
1.61E ⫹ 01
NAb
J27-1
J27-2
J27-3
J27-4
J27-5
J27-6
J27-7
J27-8
J27-9
J27-10
0.0651
0.0892
0.0495
0.0572
0.0816
0.0749
0.1029
0.1128
0.1255
0.1297
0.102
0.101
0.110
0.101
0.093
0.098
0.106
0.106
0.106
0.111
0.0029
0.0070
0.0010
0.0026
0.0074
0.0043
0.0080
0.0098
0.0143
0.0168
2.78
6.91
1.10
2.50
6.57
3.96
7.91
9.46
11.5
17.4
2.39E ⫺ 01
2.26E ⫹ 01
7.57E ⫺ 04
7.74E ⫺ 02
2.09E ⫹ 01
3.44E ⫹ 00
4.68E ⫹ 01
6.78E ⫹ 01
2.37E ⫹ 02
5.27E ⫹ 02
2.44E ⫺ 01
1.40E ⫹ 01
2.17E ⫺ 03
1.28E ⫺ 01
6.79E ⫹ 00
2.18E ⫹ 00
2.00E ⫹ 01
3.73E ⫹ 01
1.02E ⫹ 02
2.51E ⫹ 02
0.0285
0.0342
0.0362
0.0397
0.0480
0.0672
0.0667
0.0786
0.0812
0.0950
0.111
0.110
0.109
0.111
0.105
0.120
0.112
0.096
0.094
0.088
0.00059
0.00088
0.00091
0.0011
0.0017
0.0018
0.0032
0.0069
0.0077
0.0162
0.57
0.85
0.86
1.07
1.60
1.83
3.14
5.94
6.47
13.1
3.92E ⫺ 05
1.00E ⫺ 20
1.16E ⫺ 04
1.81E ⫺ 04
2.73E ⫺ 03
7.62E ⫺ 02
4.40E ⫺ 01
3.51E ⫹ 01
4.42E ⫹ 01
3.05E ⫹ 02
2.27E ⫺ 03
3.29E ⫺ 02
3.85E ⫺ 02
9.50E ⫺ 02
4.24E ⫺ 01
5.72E ⫹ 00
6.66E ⫹ 00
8.99E ⫹ 01
1.13E ⫹ 02
2.67E ⫹ 02
Run
BOMC
BOMC
BOMC
BOMC
BOMC
BOMC
BOMC
BOMC
BOMC
BOMC
a
14c
7a
14b
7b
7c
1
2
6
4
5
Read, for example, 2.09E ⫺ 04 as 2.09 ⫻ 10⫺4.
NA is not available.
b
quent runs. For these seven runs the reported velocity and
discharge per unit width are 10 –15% larger than that calculated from the Venturi measurements, and the reported bed
shear stress is 0 –3% smaller.
The bed shear stress was corrected for sidewall effects, following the method of Vanoni and Brooks [1957], as modified by
Chiew and Parker [1994]. The resulting shear stress was consistently 8% smaller than that calculated using the flow depth
and was 24% larger than that calculated using the flow hydraulic radius. Because the sediment bed was essentially planar in
almost all runs, no further adjustments were made to estimate
the mean bed stress. Long, low dunes, with an irregular slip
face and dune height smaller than 1 cm were present in the two
BOMC runs with largest flow strength, such that the estimated
shear stress in these runs includes some form drag, although
we estimate it to be a small proportion of the total bed stress.
3.3.
Bed Surface Grain-Size Distribution
All grains of each size fraction had been previously painted
a different color [Wilcock and McArdell, 1993]. This unusual
step allows us to measure the grain-size distribution of the bed
surface using point counts on photographs of the bed, which
provides a reliable and statistically tractable estimate of the
bed surface grain-size distribution. The grain-size distribution
WILCOCK ET AL.: STUDY OF TRANSPORT OF MIXED SAND AND GRAVEL
of the bed surface was measured by projecting photographs of
the bed onto a grid and tallying the grain color (hence size)
falling on the grid intersections. Each photograph covered a
bed section with dimensions of 20 cm in the cross-stream
direction and 28 cm in the downstream direction. Individual
grains were visible for all fractions. Two adjacent photographs
provided continuous cross-stream coverage of 40 cm. The remaining 10 cm on each side of the flume was not photographed. Point counts were conducted for the downstream 4 m
of the test section, and an individual surface size sample typically used 3920 points, although occasionally the number of
points counted was smaller by a few percent because the film
exposure did not permit reliable counts in small areas of the
bed. A large number of points was used in order to estimate
the proportion F i of each size fraction on the bed surface. The
grid-by-number method used here to determine the bed surface grain-size distribution has been shown to be equivalent to
the volume-by-weight method commonly used in bulk sampling and sieve analyses [Kellerhals and Bray, 1971; Church et
al., 1987]. On the basis of previous analysis of replicate point
counts and a comparison between bulk and screeded beds we
suggest that a conservative estimate of the error in measuring
F i is ⫾30% (e.g., for an observed F i ⫽ 0.1 the true value is
likely to fall within 0.07 and 0.13). The actual error in most
cases should be considerably smaller [Wilcock and McArdell,
1993].
3.4.
Experimental Procedure
The sediment bed was thoroughly mixed by hand and
screeded flat; the bed was always prepared by the same person
in order to make the initial bed as consistent as possible.
Repeated point counts of the initial screeded beds demonstrated the consistency of the initial bed surface grain-size
distribution. To save time, the sediment bed was not remixed and
screeded before each run but 3 or 4 times over the entire series of
runs with each sediment. Within a sequence of runs following
remixing and screeding, flume runs were always conducted with a
large increase in transport rate from the preceding run. Because
the sediment mobilized in any run was completely incorporated
into the much larger amount of sediment mobilized in subsequent
runs in the same sequence, the bed surface observed at the end of
each run could be attributed to the initial prepared bed and not,
for example, to a sorted surface left by a larger transport rate
[Parker and Wilcock, 1993].
A suite of hydraulic and transport measurements were made
during each run, including water discharge, surface velocity,
water and bed surface elevations, volumetric sampling of the
finer-grained transport, and mass sampling of the coarsergrained transport. At the end of the run, samples of the finegrained transport were saved for size analysis. Steady state
conditions appropriate for transport sampling were defined by
a stable mean in transport rate and size distribution. These
final samples can be correlated with the bed surface at the end
of the run. The flume was then drained, and the bed surface
was photographed. After the transport samples had been
sieved and returned to the upstream end of the flume, the
flume was filled, and another run in the sequence was begun at
a larger transport rate. After the last run in a series was completed, the bed was completely rehomogenized in preparation
for the next series of runs.
4.
4.1.
3353
Results
Bed Surface Grain-Size Distribution
The proportion of sand F s on the bed surface at the end of
runs is plotted in Figure 3a along with mean F s of the initial
beds (“Initial Bed Surface”) and the sand content f s in the bulk
mixture (“Bulk”). In general, F s is relatively insensitive to
discharge but varies systematically with f s . For J06 and J14, F s
is very small, indicating that most of the sand initially on the
bed surface was progressively stored within the pores of the
gravel mixture. Transport also reduced F s for J21 and J27,
although the decrease from its initial value is proportionately
smaller and the presence of measurable sand on the bed surface suggests that the available sand storage within the bed has
been filled. For BOMC, mean F s is 47.5%, which is comparable to that of the initial bed surface (Figure 3a). Sand content
increases with flow strength for BOMC, which Wilcock and
McArdell [1993] attributed to the associated increase in the bed
thickness actively involved in the transport. Larger flows are
able to “mine” sand from deeper in the bed. Because of the
large sand content of BOMC, only a portion of the exhumed
sand is able to return to the bed subsurface.
Similar to F s , median size (D 50 ) of the bed surface clearly
varies with f s and is less sensitive to discharge (Figure 3b). The
change in surface D 50 can be attributed in part to variation in
sand content and in part to variation in the median size of the
surface gravel D g (Figure 3c). Note that the grain-size scale on
Figures 3b and 3c is arithmetic, which tends to accentuate
minor changes in grain size, particularly at larger sizes. There
is some indication that D g increases with discharge, although
the trend is weak and noisy. In runs with BOMC we observed
that the bed was typically in a state of partial transport [Wilcock and McArdell, 1993, 1997], meaning that a portion of the
grains on the bed surface remained immobile throughout the
run. The range of sizes in a state of partial transport increased
consistently with flow strength, and full mobilization of all
grains on the bed surface (with the exception of a small portion
of the grains in the coarsest fraction) was achieved only at the
largest flow [Wilcock and McArdell, 1997]. We did not make
partial transport observations for the four new sediments, although we expect that a similar trend in partial transport occurred over the range of flow used for each sediment. Coarsening of the bed surface in a sediment recirculating flume is
predominantly through kinematic sorting [Wilcock, 2001], by
which finer grains are able to occupy space vacated by the
entraiment of large grains, but not vice versa, leading to a
downward movement of fine gains relative to coarse grains.
Because coarse grain entrainment is necessary for kinematic
sorting to operate, an increase in surface D g with flow strength
may be attributed to a corresponding increase in the proportion of coarse grains entrained during a run. We expect, but
cannot explicitly demonstrate, that D g would change little with
increases in flow strength beyond that required to mobilize the
entire bed surface.
The observation of little or no coarsening with increasing
flow strength and transport rate has important implications for
our understanding of streambed armor. A paradigm has developed that coarse armor layers evident at low flow tend to
“break up” and become finer-grained as transport rate increases [e.g., Parker and Klingeman, 1982; Dietrich et al., 1989].
This interpretation is based primarily on flume experiments in
which sediment of a constant size is fed into the flume. Under
these conditions, differences in grain mobility (which tend to
3354
WILCOCK ET AL.: STUDY OF TRANSPORT OF MIXED SAND AND GRAVEL
Figure 3. Grain-size distribution of the bed surface at the end of each run. (a) Percent sand on the bed
surface. (b) Median grain size of the bed surface. (c) Median grain size of the gravel on the bed surface (size
distribution truncated at 2 mm). Values corresponding to the bulk sediment and to the initial screeded bed
surface are shown on the left side of each panel.
vary with both grain size and flow strength) may be expected to
cause the surface to coarsen at smaller transport rates and to
become finer at larger transport rates [Parker and Klingeman,
1982]. Our results in a recirculating flume indicate that the
surface layer does not disappear as transport increases and
may actually become slightly coarser over the range of partial
transport. Inasmuch as the boundary conditions for natural
streams fall somewhere between the two end-member cases
represented by sediment feed and recirculating flumes, the
idea that armor layers vanish with increasing transport rates
does not appear to be general. Indeed, because the grain size
of the transport in natural streams tends to increase with flow
strength and transport rate, a property replicated by recircu-
lating flumes but not feed flumes, it appears likely that armor
evolution with transport rate is much more subtle than previously thought and may be negligible [Wilcock, 2001].
4.2. Gravel Transport Rates as a Function
of Sand Content
The primary objective of the experiments was to demonstrate the effect of sand content on transport rate. The variables that can be specified in a sediment recirculating flume are
the sediment placed in the bed, the mean flow depth, and the
water discharge [Parker and Wilcock, 1993]. Only sand content
varied from mixture to mixture. Variations in mean flow depth
were relatively minor, and discharge was varied from run to
WILCOCK ET AL.: STUDY OF TRANSPORT OF MIXED SAND AND GRAVEL
3355
Figure 4. Transport rates for all experimental runs. (a) Total transport rate as a function of water discharge.
(b) Total transport rate as a function of bed shear stress. (c) Gravel (⬎2 mm) transport rate as a function of
water discharge. (d) Gravel (⬎2 mm) transport rate as a function of bed shear stress. Note that gravel
transport rates are not scaled by the proportion of gravel in the bed.
run to produce different transport rates. As discharge increases, bed and water slope at equilibrium transport also
increase. In our experiments the slope remained small (maximum 0.0204), and variations in slope from run to run may be
expected to have essentially no direct effect on the transport
[Fernandez-Luque and van Beek, 1976]. With small slopes and
minor variation in flow depth a plot of transport rate versus
discharge provides a simple and direct demonstration of the
effect of sand content on transport rate. This effect is very
large, with more than a 5 order-of-magnitude increase in transport rate from J06 to (BOMC) at some values of q (Figure 4a).
Part of this increase represents rapid transport of the extra
sand added to the mixtures. Of more particular interest is the
effect of f s on the transport rate of the gravel q g . Again, the
increase in transport rate with increasing f s is very large (Figure 4c). Trends for the sandier mixtures (J21, J27, and BOMC)
fall progressively above those for the less sandy mixtures (J06
and J14), and the spread in transport rate is as much as 5
orders of magnitude at some q.
The increase in q g is all the more striking because q g in
Figure 4c is not scaled by the proportion of gravel in the bed.
As f s increases, the proportion of gravel in the mixture decreases proportionately. If sand content had no effect on gravel
transport rate, increasing the sand content should decrease the
gravel transport rate by an amount proportional to its decreased proportion in the mixture. Because the proportional
changes in gravel content are small (decreasing from 0.94 to
0.66 over the range of sediments) relative to the scale of the
transport axis, one would expect that the gravel transport rates
would fall within a single swath reflecting experimental variation. Instead, the gravel transport rates for the sandier beds fall
consistently above those of the less sandy beds. Adding sand to
the bulk mixture clearly increases the transport rate of the
gravel portion of the load.
Transport rate plotted as a function of ␶ (Figures 4b and 4d)
provides a cleaner separation of the transport trends for the
different sediment mixtures. The trend between gravel transport rate and ␶ is nearly the same for J06 and J14 and increases
consistently with increasing sand content such that at a constant ␶
the sandiest mixture (BOMC) has a transport trend 2 or more
orders of magnitude above that for J06 and J14 (Figure 4d). The
increase in qg is largest between J14 and J27 (Figure 4d).
5.
Comparison With Standard Scaling
As sand is added to a gravel mixture, the overall size distribution becomes finer. Because transport rate scales inversely
with grain size, the increase in transport rate we observe with
increasing f s might be attributed to a reduction in the grain size
of the mixture. Here we use a standard scaling of the relation
between transport rate and grain size to evaluate whether the
increases we observe in total transport rate and gravel transport rate might be predicted from the reduction in mixture
grain size.
3356
WILCOCK ET AL.: STUDY OF TRANSPORT OF MIXED SAND AND GRAVEL
Total transport rate may be scaled with the overall mixture
grain size, which can be represented using a characteristic
grain size such as the median D 50 . For unisize sediment this
relation is directly embodied in the Shields number ␶* typically
used to model transport rates
␶* ⫽
␶
,
共s ⫺ 1兲 ␳ gD 50
(1)
where s is the ratio of sediment density ␳ s to water density ␳,
g is gravitational acceleration, and ␶ is shear stress. Transport
rate is a nonlinear function of ␶*, which has led to the formulation of transport models in terms of ␶ *- ␶ * c or ␶ */ ␶ * c , where
␶ * c is the critical value of ␶* defining the threshold of sediment
transport [e.g., Meyer-Peter and Müller, 1948; Yalin, 1977]. If a
single relation between dimensionless transport rate and ␶ */
␶ * c is found to hold for sediments of different grain size,
size-dependent effects on transport are isolated to the variation of ␶ * c with grain size. For unisize sediment in the gravel
size range, ␶ * c is approximately constant, indicating that ␶ c
increases, and ␶ */ ␶ * c decreases, linearly with D. This scaling
has also been observed to hold approximately for D 5 0 of
mixed-size sediments [Wilcock, 1993].
The critical shear stress for the total transport rate of the five
mixtures can be estimated using the reference shear stress ␶ r
that produces a small dimensionless reference transport rate
W* ⫽ 0.002 [Parker et al., 1982; Wilcock, 1988] where
W* ⫽
共s ⫺ 1兲 gq b
u *3
(2)
and u * ⫽ ( ␶ / ␳ ) 0.5 . W* for the total transport rates are shown
in Figure 5a, along with values of ␶ rt used to scale ␶ in Figure
5b. The similarity collapse for the total transport rate is reasonably strong, indicating that most of the variation in transport rate from mixture to mixture is captured by ␶ rt . If the
increase in transport with increasing f s were due solely to the
reduction in D 50 , we would expect ␶ *r50 to remain relatively
constant from mixture to mixture, or to decrease slightly, following the trace of the standard unisize Shields curve (Figure
5c). Instead, ␶ *r50 decreases rapidly with decreasing D 50 , indicating that increasing f s increases total transport rate beyond
that which may be attributed to grain size alone. Using D 50 of
the bulk size distribution to form ␶ *r50 , values are close to
typical unisize values (⬇0.045) for the low sand mixtures J06
and J14 but decrease to very small values for the three sandier
mixtures, with ␶ *r50 as small as 20% of the unisize Shields
values. Scaling the Shields number using surface grain size
moderates this difference somewhat, with ␶ *r50 taking typical
surface-based values of ⬇0.035 (a 23% reduction from standard Shields values) for the low sand mixtures and decreasing
to 0.014 (a 62% reduction from Shields values) for the two
sandiest mixtures.
When considering the transport of the gravel only, comparison of observed transport rates with conventional estimates
requires accounting for the change in both relative and absolute grain size as sand content is increased. As D 50 decreases,
any gravel fraction (or the median D g of all gravel fractions
used here) becomes larger relative to D 50 . The variation of
fraction critical shear stress ␶ ci with grain size is often approximated as
␶ ci ⫽ ␶ c50
冉 冊
Di
D 50
b
,
(3)
Figure 5. Analysis of total transport rate. (a) Dimensionless
transport rate W* as a function of bed shear stress, showing the
reference value W* ⫽ 0.002 and the values of reference shear
stress ␶ rt for each mixture. (b) W* as a function of ␶ / ␶ rt , using
values of ␶ rt indicated in Figure 5a. (c) Shields number ␶ *r50
formed using ␶ rt and D 50 of either bulk or surface size distributions as a function of median grain size of bulk or surface
size distributions. D 50 increases consistently from the sandiest
mixture (bed of many colors (BOMC)) to the least sandy
mixture (J06).
where b typically takes a value between 0 and 0.3 [e.g., Parker
et al., 1982; Andrews and Parker, 1987; Wilcock, 1988, 1993].
Expressed in terms of Shields number for the reference shear
stress of gravel, this is
␶ *rg ⫽ ␶ *r50
冉 冊
Dg
D 50
b⫺1
,
(4)
indicating that adding sand will change ␶ *rg in proportion to the
change in ␶ *r50 reduced by the change in relative grain size
(D g /D 50 ). Transport rates for the gravel (Figures 6a and 6b)
collapse similarly to those for the total transport (Figures 5a
WILCOCK ET AL.: STUDY OF TRANSPORT OF MIXED SAND AND GRAVEL
3357
␶ *rg , observed values are again close to estimated values for the
low sand mixtures but fall well below estimated values for the
sandier mixtures, with the exception of BOMC. The reduction
in observed ␶ *rg is similar to the reduction in ␶ *r50 shown in
Figure 5c.
The effect of adding sand on either the total transport rate
or the gravel transport rate is evidently stronger than that
which can be estimated based on the reduction in mixture grain
size alone [Wilcock, 1998]. The increased mobility due to adding sand is captured in a reduction in the reference shear
stress, which indicates that its effect on transport rate will be
strongly nonlinear, increasing without bound as ␶* approaches
␶ * c in most standard transport formulas.
Standard scaling relations between transport rate and grain
size do not adequately represent the effect of f s on gravel
transport rate, suggesting that current models of mixed-size
transport may need to be revised. P. R. Wilcock and S. T.
Kenworthy (A two-function model for the transport of sand/
gravel mixtures, submitted to Water Resources Research, 2001)
(hereinafter referred to as Wilcock and Kenworthy, submitted
manuscript, 2001) develop the approach of Wilcock [1998] into
a model for predicting the effect of f s on gravel transport rates.
By considering the sediment as a binary mix of two fractions,
sand and gravel, the model can account for the effect of f s on
transport in a simple and direct manner.
6.
Figure 6. Analysis of gravel transport rate. (a) Dimensionless
gravel transport rate W *g as a function of bed shear stress,
showing the reference value W *g ⫽ 0.002 and the values of
reference shear stress ␶ rg for each mixture. (b) W *g as a function of ␶ / ␶ rg , using values of ␶ rg indicated in Figure 6a. (c)
Shields number ␶ *rg formed using ␶ rg and D g of either bulk or
surface size distributions as a function of relative grain size
D g /D 50 based on either bulk or surface size distributions.
D g /D 50 increases consistently from the least sandy mixture
(J06) to the sandiest mixture (BOMC). Curves are equation
(4) using ␶ *r50 of 0.045 and 0.035.
and 6b), indicating that ␶ *rg captures most of the sand effect on
gravel transport rates. Observed values of ␶ *rg are given in
Figure 6c, along with estimates of ␶ *rg from (4) using ␶ *r50 ⫽
0.045 (typical for subsurface grain size) and ␶ *r50 ⫽ 0.035
(typical for surface grain size) and b ⫽ 0 and b ⫽ 0.3,
bracketing typical values of these parameters. For ␶ *rg formed
using D g of the bulk size distribution, observed values are
similar to estimated values for the low sand mixtures J06 and
J14 but drop well below the estimated values for the sandier
mixtures. When the surface size distribution is used to form
Discussion
A variety of processes (e.g., logging, fire, land development,
and reservoir flushing) can increase the supply of fine sediment
to a gravel bed river. If this causes f s of the river bed to
increase, our results indicate that the transport capacity for
both sand and gravel will increase, which can limit the magnitude of channel adjustment to the increased sediment supply
and may also cause the r iver to evacuate the excess sediment
in a shorter time than would be estimated from conventional
models. Application of these results to the field requires a
model that generalizes the experimental results given here, and
further discussion is given by Wilcock and Kenworthy (submitted mansuscript, 2001), who present such a model.
Application of our results to the field also requires specifying
a size boundary between fine and coarse sediment. The threshold used here is 2 mm. Although this is the standard boundary
between sand and gravel and represents an appropriate boundary in many field cases, it is essentially arbitrary. We expect
that a larger boundary would be appropriate for some coarser
sediments. For example, we have used a boundary of 8 mm on
a coarse gravel/cobble river with a distinct fine mode in the
sand and pea gravel range [Wilcock et al., 1996]. Further discussion of the choice of size boundary is given by Wilcock and
Kenworthy (submitted manuscript, 2001), which interprets the
effect on transport rate of fines content in terms of the relative
proportion of matrix and framework grains.
7.
Conclusions
Transport measurements using five sediments with different
sand content indicate that total transport rate and gravel transport rate depend strongly on sand content. The effect of sand
content on transport was isolated by using the same gravel
population and varying only the proportion of sand from mixture to mixture. Flow depth was also held within a narrow
range, and discharge was varied to produce a wide range of
3358
WILCOCK ET AL.: STUDY OF TRANSPORT OF MIXED SAND AND GRAVEL
transport rates with each sediment. For the same flow strength
we observe that gravel transport rates increase by orders of
magnitude as sand content is increased, despite the fact that
the amount of gravel available for transport decreases as sand
content increases. The increase in gravel transport rate is most
rapid between the mixtures containing 14, 21, and 27% sand,
which corresponds approximately to the transition from a
framework-supported to a matrix-supported sediment bed.
These results support and extend earlier observations of an
increase in gravel transport rate with increasing sand content.
The present experiments use sediment with a wide range of
sizes representative of many gravel bed streams and a sediment-recirculating arrangement that allows a direct correlation
between bed composition and transport rate.
The bed surface composition was measured at the end of
each run, providing a set of coupled flow/transport/bed surface
observations for a wide range of transport rates with all five
sediment mixtures. These data provide the opportunity to explore mixed-size transport models referenced to the bed surface, an essential component of a general model capable of
predicting transient conditions. The bed surface grain size varies strongly with sand content but shows little or no coarsening
with flow strength. This casts doubt on the idea that armor
layers form at small flows and weaken or vanish with increasing
flow and transport rate. As flow strength increases, the minor
surface coarsening we observe may be attributed to the entrainment of an increasing proportion of coarse grains from
the bed surface. This increases the opportunity for coarsening
through kinematic sorting, the primary mechanism by which
recirculating flume beds may armor.
The effect of sand content on transport rate is larger than
would be predicted using standard scaling relations between
transport rate and the reduction in grain size associated with
increasing sand content. Models of mixed-size transport and of
stream channel response to varying sediment inputs require
revision to account for the influence of variable sand content.
The effect of sand content on transport rate may be largely
isolated to its effect on the critical shear stress for incipient
motion. A model that includes the effect of sand content on
sand and gravel incipient motion is proposed by Wilcock and
Kenworthy (submitted manuscript, 2001).
Acknowledgments. This work was funded by the U.S. Department
of Justice, Environment and Natural Resources Division. Conversations with Bill Emmett, Jack King, Gary Parker, Larry Schmidt, Peter
Whiting, and Reds Wolman helped refine our analysis.
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(Received May 10, 2001; revised August 28, 2001;
accepted August 30, 2001.)